means to look at something attentively over a stretch of time, or the small timepiece you wear to track that time slipping by.

from From Old English 'wæccan,' to keep awake or stay alert — a sibling of 'wake.' For centuries a 'watch' was a vigil or a shift of guards staying alert through the night, and the night itself was divided into 'watches.' Only later, around the 16th century, did the name pass to the small spring-driven clock you could keep with you — likely because it, too, was always awake and ticking.